A261015 Irregular triangle read by rows: T(n,k) (0 <= k <= 2^n-1) = number of binary strings of length n such that the smallest number whose binary representation is not visible in the string is k.

1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 0, 0, 0, 1, 1, 3, 6, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 4, 11, 10, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 5, 19, 21, 15, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

N. J. A. Sloane, Aug 16 2015

Keywords

• nonn
• tabf

Comments

Suggested by A260273.

Examples

			Triangle begins:
  1,1,
  1,1,1,1,
  1,1,2,3,1,0,0,0,
  1,1,3,6,4,1,0,0,0,0,0,0,0,0,0,0,
...
For row 3, here are the 8 strings of length 3 and for each one, the smallest missing number k:
 000 1
 001 2
 010 3
 011 2
 100 3
 101 3
 110 4
 111 0
		

Links

• Alois P. Heinz, Rows n = 1..15, flattened

Crossrefs

Cf. A260273, A261016, A261017.

See A261019 for a more compact version (which has further information about the columns).

Programs

Mathematica

notVis[bits_] := For[i = 0, True, i++, If[SequencePosition[bits, IntegerDigits[i, 2]] == {}, Return[i]]];
T[n_, k_] := Select[Rest[IntegerDigits[#, 2]]& /@ Range[2^n, 2^(n+1)-1], notVis[#] == k&] // Length;
Table[T[n, k], {n, 1, 6}, {k, 0, 2^n-1}] // Flatten (* Jean-François Alcover, Aug 02 2018 *)

Extensions

More terms from Alois P. Heinz, Aug 17 2015